Uniqueness of the electrostatic solution in Schwarzschild space

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.Comment: 3 pages, no figures, uses revtex4 style file

The prismatic Sigma 3 (10-10) twin bounday in alpha-Al2O3 investigated by density functional theory and transmission electron microscopy

The microscopic structure of a prismatic $\Sigma 3$ $(10\bar{1}0)$ twin boundary in \aal2o3 is characterized theoretically by ab-initio local-density-functional theory, and experimentally by spatial-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope (STEM), measuring energy-loss near-edge structures (ELNES) of the oxygen $K$-ionization edge. Theoretically, two distinct microscopic variants for this twin interface with low interface energies are derived and analysed. Experimentally, it is demonstrated that the spatial and energetical resolutions of present high-performance STEM instruments are insufficient to discriminate the subtle differences of the two proposed interface variants. It is predicted that for the currently developed next generation of analytical electron microscopes the prismatic twin interface will provide a promising benchmark case to demonstrate the achievement of ELNES with spatial resolution of individual atom columns

High speed laser tomography system

Article / Letter to editorLeiden Institute of Chemistr

Parallel Search with no Coordination

We consider a parallel version of a classical Bayesian search problem. $k$ agents are looking for a treasure that is placed in one of the boxes indexed by $\mathbb{N}^+$ according to a known distribution $p$. The aim is to minimize the expected time until the first agent finds it. Searchers run in parallel where at each time step each searcher can "peek" into a box. A basic family of algorithms which are inherently robust is \emph{non-coordinating} algorithms. Such algorithms act independently at each searcher, differing only by their probabilistic choices. We are interested in the price incurred by employing such algorithms when compared with the case of full coordination. We first show that there exists a non-coordination algorithm, that knowing only the relative likelihood of boxes according to $p$, has expected running time of at most $10+4(1+\frac{1}{k})^2 T$, where $T$ is the expected running time of the best fully coordinated algorithm. This result is obtained by applying a refined version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in STOC'16, which was designed for the context of linear parallel search.We then describe an optimal non-coordinating algorithm for the case where the distribution $p$ is known. The running time of this algorithm is difficult to analyse in general, but we calculate it for several examples. In the case where $p$ is uniform over a finite set of boxes, then the algorithm just checks boxes uniformly at random among all non-checked boxes and is essentially $2$ times worse than the coordinating algorithm.We also show simple algorithms for Pareto distributions over $M$ boxes. That is, in the case where $p(x) \sim 1/x^b$ for $0< b < 1$, we suggest the following algorithm: at step $t$ choose uniformly from the boxes unchecked in ${1, . . . ,min(M, \lfloor t/\sigma\rfloor)}$, where $\sigma = b/(b + k - 1)$. It turns out this algorithm is asymptotically optimal, and runs about $2+b$ times worse than the case of full coordination

First-principles study of spontaneous polarization in multiferroic BiFeO3_3

The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation.Comment: (9 pages, 5 figures, 5 tables

The Sigma 13 (10-14) twin in alpha-Al2O3: A model for a general grain boundary

The atomistic structure and energetics of the Sigma 13 (10-14)[1-210] symmetrical tilt grain boundary in alpha-Al2O3 are studied by first-principles calculations based on the local-density-functional theory with a mixed-basis pseudopotential method. Three configurations, stable with respect to intergranular cleavage, are identified: one Al-terminated glide-mirror twin boundary, and two O-terminated twin boundaries, with glide-mirror and two-fold screw-rotation symmetries, respectively. Their relative energetics as a function of axial grain separation are described, and the local electronic structure and bonding are analysed. The Al-terminated variant is predicted to be the most stable one, confirming previous empirical calculations, but in contrast with high-resolution transmission electron microscopy observations on high-purity diffusion-bonded bicrystals, which resulted in an O-terminated structure. An explanation of this discrepancy is proposed, based on the different relative energetics of the internal interfaces with respect to the free surfaces

Bond-order potential for simulations of extended defects in tungsten

We present a bond-order potential (BOP) for the bcc transition metal tungsten. The bond-order potentials are a real-space semiempirical scheme for the description of interatomic interactions based on the tight-binding approximation. In the hierarchy of atomic-scale-modeling methods the BOPs thus provide a direct bridge between electronic-structure and atomistic techniques. Two variants of the BOP were constructed and extensively tested against accurate first-principles methods in order to assess the potentials\u27 reliability and applicability. A comparison of the BOP with a central-force potential is used to demonstrate that a correct description of directional mixed covalent and metallic bonds is crucial for a successful and fully transferable model. The potentials are applied in studies of low-index surfaces, symmetrical tilt grain boundaries, and dislocations

Parametric excitation of plasma waves by gravitational radiation

We consider the parametric excitation of a Langmuir wave and an electromagnetic wave by gravitational radiation, in a thin plasma on a Minkowski background. We calculate the coupling coefficients starting from a kinetic description, and the growth rate of the instability is found. The Manley-Rowe relations are fulfilled only in the limit of a cold plasma. As a consequence, it is generally difficult to view the process quantum mechanically, i.e. as the decay of a graviton into a photon and a plasmon. Finally we discuss the relevance of our investigation to realistic physical situations.Comment: 5 pages, REVTe